Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

264 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
1
vote
0answers
1k views

Black-76 Model for Swaption Price and Greeks

I'm in the early stages of developing a swaption pricing model. Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
1
vote
0answers
82 views

Calibrating Heston paremeters based on market data for Implied Vol for Call options

Several questions have been asked in here regarding calibration in Heston yet I have not found what I have been looking for, so I will ask: I am looking at a Heston model: $$dS_t=\lambda \sqrt{v_t}...
1
vote
0answers
91 views

Beta of options based strategy

This is probably a simple/dumb question, but I am not getting it. As per GMO's recent Insight: Second, as can be inferred from Exhibit 1, put writing strategies have a low beta to the equity ...
1
vote
0answers
42 views

Sub-Optimal exercise

I have seen exercise multiples applied to account for sub-optimal exercise of American style options in the case of employee share schemes (as the employees are irrational). I would like to know if ...
1
vote
0answers
46 views

Low estimator when valuing american option using Broadie and Glassermann Monte Carlo tree with antithetic branching (R)

I've been looking into Monte Carlo methods for valuing american options. Now, I found an R code by Stefano M. Iacus that values the option using a tree (based on Broadie and Glassermann) without use ...
1
vote
0answers
97 views

Price futures option via replication

I ran into some difficulties when trying to price a futures option via replication in a simple one-period binomial model. I am quite aware that this is easy with risk-neutral probabilities and ...
1
vote
0answers
39 views

Evaluating contract $D$ where the stock follows the Black Scholes assumption

Ch.7 Mark Joshi Problem 14 A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
1
vote
0answers
125 views

Constant volatility and risk-free rate assumptions of Black Scholes

I'm studying the risk-neutral derivation of Black-Scholes formula and feel confused about the requirement for the volatility of the underlying asset and the risk-free rate to be constant. It seems ...
1
vote
0answers
241 views

Convexity of Call option prices using Put-Call parity relationship

I am trying to price vanilla options using a particular Bayesian approach that I have found in a paper. To do that I need to construct a likelihood function, approximating the tail of the distribution ...
1
vote
0answers
30 views

Option style with grant date

The following option exercise style is somewhere between American and European: There is a fixed grant date $N_1$ at which you determine at which date $N_2>N_1$ the option will be exercised. So ...
1
vote
0answers
471 views

Dividend yield for an index

Let's say we want to price an option and so need a dividend yield to plug into Black-Scholes. We can compute an implied dividend yield for a stock using: $$F=S_0 e^{(r-d)T}$$ and by isolating for $...
1
vote
0answers
186 views

Time frame for implied vs realized vol

I've seen charts of implied vol (IV) against realized volatility? What time frames do people generally use to calculate each? For example, do people generally use ATM 1 month call options to get IV, ...
1
vote
0answers
1k views

How to derive the Greek theta from Black-Scholes solution formula?

Which are the steps to compute the theta greek from the BS solution: $$c(t, x) = xN(d_+(T-t,x)) - K e ^{-r(T-t)}N(d_-(T-t,x))$$ with: $$ d_\pm (T-t, x) = \dfrac{1}{\sigma \sqrt{T-t}} \left[ \ln \...
1
vote
0answers
68 views

gamma-weighted SOIR

I came across a term 'gamma-weighted SOIR' several times recently. it seem like an old term on gamma imbalance. could someone care to explain what this is and the rationale behind it?
1
vote
0answers
61 views

The interpretation of discounted Greeks

I understand that Delta measures the rate of change of the theoretical option value with respect to the change of the underlying asset price. This also represents the number of shares a call option ...
1
vote
0answers
1k views

Short Call Hedge. Options and gamma trading

Let’s say a trader sells a Short Call with strike 100 (for making profit with the premium) at-the-money (for highest extrinsic value there). For hedging until expiration, he buys the underlying share ...
1
vote
0answers
112 views

Mean correcting martingale argument

Let $X=(X_t,t\in\mathbb{N})$ be a pure jump Lévy process (i.e $X_t$ does not have a diffusion component). Let further $Y=(Y_t,t\in\mathbb{N})$ be a process that is used to time-change the process $X$ (...
1
vote
1answer
261 views

Exercise Probabilities Vanilla Cap/Foor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
1
vote
0answers
39 views

Rigorous definition of the two values of a European call

Assume a BS model. For a European call option with strike $K$ and expiry $T$, its intrinsical value at time $t$ is defined to be $(S_t-K)_+$ i.e. the payoff we could get if we immediately exercised ...
1
vote
0answers
36 views

Floor option EVE risk: Sum of key rate shocks risks vs. the rates parallel shock risk

Consider a model measuring the EVE risk (change in the economic value by shocking the rates; PV01) of a portfolio of vanilla interest rate floor options. Is there any reason for the EVE risk of a ...
1
vote
0answers
115 views

When to expect profitability of a call options buying strategy

When could we expect consistent profitability of a call options buying strategy given specific statistical assumptions about X% chance of a stock price moving up by Y% within 1-5 days (or Z number of ...
1
vote
0answers
149 views

R/fOptions Binomial Options Pricing warning message

Trying to compute theoretical prices for a set of options using the R package fOptions: ...
1
vote
0answers
156 views

Pricing Asian option at discrete times

I hope you can help me again regarding pricing an arithmetic Asian option. Asumme we have a time grid $(0=t_0,t_1,t_2=T)$ and we buy an Asian option at time 0 and the maturity is at T. Now we would ...
1
vote
0answers
114 views

commodity futures options data

I am trying to get my hands on some historical commodity futures options data for about 35 commodity futures. So far in my search the only way I can get the data seems to be through the Commodity ...
1
vote
0answers
144 views

Why is shorting (oil) futures a bit of a negative gamma trade?

From this article, http://www.zerohedge.com/news/2017-01-22/oil-speculators-have-never-been-long, "I get what you're saying about the price risk which is always the danger of shorting crude oil it's ...
1
vote
0answers
52 views

How to find the ideal options trade given certain return distribution?

Suppose I have a probability distribution for the return of a given stock from now until some expiration date. Is there any algorithm/process/software that will take that probability distribution and ...
1
vote
0answers
212 views

How to calculate the volatility of a equity option spread

I would like to calculate the volatility of an equity option spread with all legs having the same expiration. Reading Option Volatility and Pricing 2nd Edition by Natenberg, Chapter 20, section ...
1
vote
0answers
232 views

Backtesting with option

More of a general question: is there anything there like a software to have any meaningful backtesting done on US equities with options in portfolios. Looking more of an off shelf product or open ...
1
vote
0answers
46 views

How to reduce data dependence for empirically assessing option pricing model performance?

I am preparing a paper about mitigating assessment failures for option pricing models. For the sake of simpliciy, suppose we are talkin about European options. In basic terms, what I would like to say ...
1
vote
0answers
239 views

Pricing Exotic options

I am stuck at a assignment problem where I have to compute the price of an exotic option. I am given the values the prices of option $C(X;k) = E[max(0,X_T - k)]$ for different strike prices $k$ and ...
1
vote
4answers
277 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
1
vote
0answers
68 views

How can I drive FPDE of American Option Price from FMLS Model?

Under the risk neutral measure $\mathbb{Q}$. The FMLS model assumes that the log value of the underlying i.e., $\bar{x}_t=\ln S_t$. with dividend yield $D$ follows a stochastic differential equation ...
1
vote
0answers
109 views

Can someone try this Boundary Condition for the Black-Scholes PDE out for me?

I have a bit of a favor to ask and if anyone could help me out with this I'd really appreciate it. At the moment I'm trying to use the triangle wave formula as the payoff for the Black-Scholes PDE i.e....
1
vote
0answers
150 views

How to calculate implied borrow rates from option chain information?

I am given information about a ticker with following options data: stock price, date, expiration date, strike price, call / put indicator, style (American or European), ask price, bid price, mean ...
1
vote
0answers
124 views

How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model

Here are two questions related to implied volatilities. a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also ...
1
vote
0answers
111 views

Is it possible to place hidden order inside spread when trading E-mini S&P 500?

My question is not about hidden orders in general. In equity market a trader can post his hidden order inside spread, is it the same way for E-mini S&P 500?
1
vote
0answers
52 views

Pricing with-profit/smoothed bonus annuity using Black-Scholes

Would this be possible? Subsequently, would the pricing of such an annuity be somewhat similar to pricing a lookback option?
1
vote
0answers
16 views

EMTA Guidelines

Does EMTA guidelines are only for Non-Deliverable trades? IF yes, then why this is applicable for Deliverable Option trades? EMTA Site - http://www.emta.org/ndftt.aspx
1
vote
0answers
55 views

Effect of surprise dividends on options

The ETF in question is VDC It pays about $2.5 a year in dividends, but the payout dates are very erratic If I were to go long VDC with options, what would be the best way of doing this to avoid ...
1
vote
0answers
80 views

Delta of an option in two cases

Let C be the prime of a call in fi=unction of the price in term F, Strike K, volatilité $\sigma$ and maturity t: $C(F,K,\sigma,t,r) $ We assume that we know $\delta$ $\delta=\frac{\partial}{\...
1
vote
0answers
74 views

How was this probability of negative U.S rates by end 2017 calculated?

http://www.bloomberg.com/news/articles/2016-01-26/bets-on-negative-u-s-rates-by-end-2017-jump-above-10-chance Options markets show some investors are taking out protection in case rates instead ...
1
vote
0answers
120 views

Gil-Palaez Inversion Formula in Black Scholes world

I am trying to calculate numerically the price of a plain vanilla call through Fourier Transform, by applying the Gil-Pelaez formula. More precisely, we have that \begin{equation} C(K) = S_0 \Pi_1 - ...
1
vote
0answers
224 views

Computation of option vega under CEV

It is easy to define the option vega $\nu=\frac{\partial C}{\partial \sigma}$ under Black Scholes model since volatility is a single quantity. However, under CEV or local volaility model, it is ...
1
vote
0answers
99 views

Cointegration and variance of time series

Given that $X_t , Y_t$ are two cointegrated random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a given $h>0$...
1
vote
0answers
167 views

Black Scholes Model Replicating Strategy Delta Hedged Exam Question

A share is currently priced at 640p. A writer of 100,000 units of a one year European put option with an exercise price of 630p has delta-hedged the option with a portfolio which holds cash and is ...
1
vote
0answers
111 views

Calculate minimum IV increase to offset theta

How would one calculate the minimum implied volatility increase necessary to offset theta decay? IV is typically a percentage, while theta is a dollar value. In theory I think I could look at what ...
1
vote
0answers
93 views

Hedge volatility decreases

My particular options positions are typically a long delta, and long vega. Decreases in implied volatility, or specifically the VIX, can drastically alter the profitability of my position. Is there a ...
1
vote
0answers
125 views

Straddle neutral strategy

What does it mean to implement a delta-neutral strategy for straddle ? A straddle consists in buying a call and a put simultaneously, at the same date, on same underlying, with same maturity and ...
1
vote
0answers
83 views

Opposite of hard to borrow?

If market participants are certain a stock will suffer a huge decline, the shares will become hard to borrow and an interest fee will be applied to borrow the stock. This interest fee eliminates the ...
1
vote
0answers
1k views

where to find historical option prices?

I have a dataset of options (traded in European exchanges such as NYSE Euronext) and I would like to find their price history. Where to find it? I see that ...